A computer game without a computer

When I was around 13 years old there was this guy in my class whose name I cannot for the life of me remember. But I do remember that he was brilliant – off the charts brilliant – and that he shared my love for all things mathematical. He also had abnormally large thumbs. Which might not be important, but it seems worth mentioning.

One day he introduced me to a game which I later realized was one of the best computer games I’ve ever played – except that it did not require a computer.

The idea was simple: Start with a piece of graph paper. Draw a picture of a race track on the graph paper. Make sure to draw a line showing the starting line and another line showing the finish line. Then place two “racers” on the paper – pencil marks denoting some starting position.

Here are the rules: At every move, your racer is allowed to accelerate in either X (left/right)) or Y (up/down) by either -1, 0, or +1. So if your racer was travelling at a speed of, say, (1, 2) in the previous move, then it can now travel between 0 and 2 units in X, and between 1 and 3 units in Y.

You need to get your racer around the track first – before your opponent gets his racer around the track – without going outside of the race track boundaries.

One thing that makes this game so cool is that slight variations in how you draw the outline of the racetrack can result in big changes in the best path around the track.

In the above picture, the track is shown in black. The two “racers”, about to start their way around the track, are shown, respectively, in red and green.

So here was a “computer game” without computers. By playing it we learned about velocity, accelaration and strategic planning. And it cost only about two cents a game – the cost of a sheet of fresh graph paper.

Inside dentist jokes

I was at the dentist this week, with nothing in particular to do except sit back, watch all the flashing and whirring equipment, and hope that the local anaesthetic would continue working. While I freely admit that the injection of feel-good chemicals may have clouded my thinking, it does not completely account for the fact that my mind was turning to thoughts of Woody Allen.

Not just any thoughts of Woody Allen, mind you, but specifically thoughts about a moment in his 2006 comedy “Scoop” in which Scarlett Johansson is playing a dental hygenicist who has reinvented herself as an investigative journalist.

The particular moment I flashed on, while desperately trying to ignore the very loud vibrating drill in my mouth, was when Ms. Johansson’s character, trying to distract the bad guy with some improvised femme fatale patter, started talking about “the lower sixth” – suddenly reverting to her inner dental hygenicist.

It happens that I had seen my dentist the day after seeing this film, and I’d mentioned that Woody Allen was making dentist jokes, relating this little bit of dialog. My dentist replied that it was a very odd dentist joke, since the sixth is actually an upper tooth. There is no lower sixth.

Now, I’m pretty sure that Woody Allen knows this perfectly well. He’s been exploring the humor in dentistry at least since his wonderful essay “If the Impressionists had been Dentists” (in “Without Feathers”, 1975). So just what is he up to here?

My theory is that it’s an inside joke – a deliberate shout-out to dentists. He’s telling them “This one’s for you. Nobody will get this joke who isn’t a dentist. Just wanted you guys to know I was thinking about you.” What makers of computer games call an “Easter Egg” – a hidden message that is visible only if you have some inside knowledge about where to look.

And this makes me wonder – how many other examples are there out there in popular books and films? What coded messages for just the few are hiding in plain sight, snuck in there by an artist, just for the fun of it? The Mickey Mouse head near the end of TRON comes to mind, but to me Woody Allen’s “lower sixth” joke seems a lot weirder – perversely surreal – and therefore more fun.

Yes, yes I know

Yes, yes I know that we’ve got a good head of steam going with this discussion about programming languages, and we will get back to it, I promise. But I feel in need of a day off from serious conversation.

And so today I will just ask the following question: Why is it that Zachary Quinto, as the monstrous Syler on the TV show “Heroes”, reminds me so damned much of Leonard Cohen?

This just seems wrong. Very, very wrong…

Talking to computers, revisited

Back to our old friend Fibonacci, poised precariously between human conversation and computer programming. The more I think about the Fibonacci sequence as a way in to the question of a lingua franca for introducing people to ideas about how to program, the more intriguing it gets.

In this post I’m going to write things mathematically, foregoing the wordy english versions, since I think we’re all agreed that the concepts are what ultimately matter here, not the syntax. Once we’ve worked out the best conceptual approaches, then we can go back and make things more “natural-language friendly”.

One question that comes up is how soon you should introduce variables. When you say:

    F(n)   ←   if   n ≤ 1   then   n   else   F(n-1)+F(n-2)

you are assuming your student is ready to understand and use variables like “n”.

In contrast, here is a description of the Fibonacci sequence without variables, stated as two “production rules”:
    F   ←   [ 0 , 1 ]

    F   ←   F   append   Flast + Flast-1

This doesn’t just return a number – it builds the whole sequence. Is this approach conceptually clearer and more intuitive? Is it closer to the way people already think?


Buddhism warns against embracing joy uncritically, without understanding its consequences. The joy that we get from each other, from human connectedness and the feeling that we are not alone, is a wondrous thing, but it also opens us up to the possibility of pain.

For with any joy comes a desire to continue that joy. And any desire creates the possibility of despair and loss. The greater is our need for connection, the more vulnerable we might be to the potential for pain.

In the West we generally don’t question the costs of our desire for joy. “Happiness is good” is a given, built into our culture like a birthright, and therefore into each individual psyche. The “third way” of Buddhism – to seek to forge a path through life that accepts joy, but is more consciously aware of the potential danger, is slightly alien to our general cultural priorities.

I often wish I were better prepared to dive into the Buddhist way of thinking from time to time – to have the mindfulness to emotionally distance myself from both my joy and my desire, so that I can see things clearly for what they are, unclouded by the fear of loss, and thereby make better choices.

Talking to computers

Suppose I described to you the following procedure (let’s call this statement 1):

        Start with the sequence 1, 1.
        Keep adding more numbers to the sequence,
        always by summing the last two numbers.

If you started following this procedure, you’d gradually get a longer and longer sequence:

1 + 1 →2
1    1 + 2 →3
1    1    2 + 3 →5
1    1    2    3 + 5 →8

You might recognize this as the procedure for creating the sequence of Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13 … a sequence that is very useful because it describes all kinds of things in nature, such as the way populations grow, the spiraling pattern on a sunflower, and the shapes of seashells and galaxies, to mention just a few.

If I just want the nth Fibonacci number, I might say things slightly differently (let’s call this statement 2):

If n is 1 or less, the answer is 1.

    add the (n-1)th and (n-2)th Fibonacci numbers.

I’m guessing that everyone reading this post will be able to understand the above statement just fine, after looking at it for a few moments.

Here is how I might convey the above statement to a computer (let’s call this statement 3):

            if n ≤ 1 then
                fibonacci(n-1) + fibonacci(n-2)

Statement 3 – the one that looks like a computer program – is exactly the same as statement 2, except that writing it as a program makes it a little easier for a computer to read.

So here’s my question: Assuming we would like to put the power of programming into the hands of everybody (the way we already try to put the power of written language into everybody’s hands), would it be worthwhile to get millions of people to learn things like statement 3 – the one that looks like programming?

Or should we get both people and computers to understand statement 2 – ie: the same statement, except written out in English? Or should we work really really hard and try to figure out how to get computers to understand statement 1 – the one at the very top of this post?

Unfortunately, if you opt for choosing statement 1, you might have to wait a very long time. That kind of casual natural language description is fairly beyond what people have been able to get computers to understand. The reason is that even simple statements like “summing the last two numbers” tend to stump a computer. An inference that would seem immediately obvious to us humans, like the fact that we are referring to the last two numbers in the sequence, is incredibly difficult for a computer to work out. Computers lack our ability to figure things out from context.

I find myself wondering whether the big leap for most people would be going from statement 1 to statement 2, or going from statement 2 to statement 3. Whereas statement 1 just kind of assumes you can fill in the parts that are unsaid, statement 2 really spells things out in a way even a computer could understand. And that’s the leap that might be hard for people.

I suspect that the real hurdle might not be teaching people to read things that look like computer programming, but rather teaching people to think in a way that makes it possible to program – the kind of step-by-step way of thinking about a problem that makes it possible to get a computer to do our bidding.

When elevators go bad

Elevator etiquette generally dictates that you pretend the other passengers are not there. Here you are, trapped together in a little box with a gaggle of complete strangers, and you are all trying not to stare at each other. For some reason, people feel this unspoken taboo quite strongly, through a kind of osmotic consensus.

Things get subtly stranger as the elevator gradually fills up. The more people there are in the elevator, the more directions there are for each of you to avoid looking. The important thing is not to accidentally acknowledge anybody else, since this would certainly bring down some terrible wrath from the Gods, and most likely end all reality and existence as we know it.

But when you are entering the elevator with a friend or colleague, there is the time-worn strategy of continuing the conversation that you and they had been holding before you’d entered the elevator. As a group of two or three people, empowered by numbers, you can just pretend that the elevator ride isn’t happening, whilst you and your colleagues and amigos make your collective way down to that sandwich shop around the corner.

In its own way, it’s a brilliant solution. Why not simply collectively ignore this unfortunate detour into civilization’s little chamber of vertical alienation? Why not just continue discussing Kierkegaard, or that Simpson’s episode, or that Simpson’s episode about Kierkegaard? Before you know it, the doors will open and you can all escape back to reality.

Which is all well and good, until another group of likeminded comrades enters from another floor, with pretty much the same idea in mind. They bring their conversation to the elevator, pointedly ignoring the presence of your group. Meanwhile, after the briefest of pauses while your group sizes up these rude upstarts, you and your friends resume your conversation, perhaps just a bit louder than a moment before.

This strange ritual continues all the way down to the lobby. For if the sound of two individuals ignoring each other in a tiny space is silence, the sound of two groups of people ignoring each other in that same little space is cacophony.

When at last the elevator door opens, both groups pour out and continue their respective conversations, each carefully failing to acknowledge that anything at all has just happened.

But something has.

Shakespeare gets a date

Today is quite a calendar day for William Shakespeare. The great playwrite was born on April 23 1564, and passed away exactly fifty two years later, on April 23 1616. Oddly, even though Miguel Cervantes, Mr. Shakespeare’s great Spanish contemporary, also died on April 23 1616, Shakespeare’s outlived Cervantes by ten days.

This is due entirely to the fact that Cervantes died in a Catholic country, where people actually paid attention to Papal edicts. Spain had already switched over to the new-fangled Gregorian calendar, whereas England would not desert the Julian calendar (which had worked great in Caesar’s time, but over the centuries was gradually drifting out of sync with the seasons) until 1752.

The British may simply not have noticed the ever increasing oddness of the seasons, since what the English call “summer” is what most people in the world generally refer to as “winter”. Consistent with this theory, Russia – which is even further north than England – did not adopt the corrected calendar until 1918 – and even then a violent Communist takeover was required. The Russians clearly take their calendar reform very seriously.

All of which would probably have seemed very amusing to Mr. Shakespeare. When I was in high school the teachers tried to get us interested in Shakespeare. Oh how they tried. It was all a complete waste of time – somewhat like trying to get your dog to watch TV. We would just roll our eyes and pretend to pay attention.

Interestingly, two years later when I transferred to Harvard I suddenly became completely smitten with Shakespeare. I developed a deep love and devotion for the comedies, the tragedies, the historical plays, the sonnets, even the hokey Zeffirelli movies.

I suspect that this sudden interest was strongly related to the fact that lots of the Radcliffe girls were really into Shakespeare. Showing up for the Immortal Bard was a great opportunity to hang out with really cute female classmates. Actually appreciating Shakespeare scored you even more points.

By the time I graduated, sure enough I had developed a true and lifelong love for all things Shakespearean. In a later era of history – centuries after the Elizabethan age – this process would come to be known as “transference”. No offense to Sigmund Freud, but I’m pretty sure there is nothing about transference that Bottom the Weaver couldn’t have told you after spending a night with Queen Titania. 😉

Earth Day in New York

I’ve been thinking about the rather odd fact that by living in the heart of Manhattan I am actually living the “greenest” American lifestyle. Strangely, it turns out that when you live in a crazily dense metropolis such as ours, you consume remarkably little energy.

You walk everywhere (or otherwise, mainly taking the subway), you don’t own a car, you carry your groceries home from a place right around the corner, to which goods had been shipped efficiently in bulk (at low energy cost per consumer), the heat to warm your apartment in winter also warms the apartments around you (rather than dissipating out through a roof) – the list of energy savings from densely packed living goes on and on.

It would be, quite literally, impossible for anyone owning a car and a house, no matter how conscientious or responsible, to achieve as eco-friendly a lifestyle as the average New Yorker obliviously going about life in Manhattan.

This situation highlights an odd contradiction between perception and reality. In our society you don’t get “goodness” points for making the best choices – you get those points for having the best attitude about your choices. Nobody pats Manhattanites on the back and says “Hey, way to go – thanks for helping to save our planet!” Because they know Manhattanites aren’t working for it. We happen to live in a highly earth-friendly way compared with other Americans – but there’s no effort going on.

And sure enough, I confess to feeling no sense of accomplishment about my naturally green lifestyle. I do sometimes feel bad for all those millions and millions of people in the U.S. who don’t get to live in Manhattan. But for entirely different reasons.


Two movies

This last weekend I saw two movies that were perfect opposites. They weren’t even oil and water, they were more like oil and armadillo. One was Tamara Jenkins’ exquisite indie film “The Savages”. The other was the Adam Sandler vehicle “You Don’t Mess with the Zohan.”

I enjoyed both thoroughly, and I found myself thinking what an amazing world this is, where a viewer can access, and heartily enjoy, two such disparate forms of entertainment. For those of you who haven’t seen it, “The Savages” is a dark, subtle character study, somehow Brechtian and romantic all at once. With the finest acting duo you might ever see on screen – Philip Seymour Hoffman and Laura Linney – making beautiful dystopian music together. Every scene between them is a study in perfection, built upon carefully woven layers of close psychological observation and misdirection. Beautiful and deeply moving, like a Mahler symphony.

“Zohan”, on the other hand, is not so much a Mahler symphony as a Silly Symphony. Rude, crude, and in your face funny, it smashes its comic target square on the jaw and keeps on punching. Ostensibly a comic farce about an Israeli counterterrorist, it’s actually about the U.S., and our country’s strange fantasies and misguided notions about Zionists, Palestinians, the conflict in the Middle East, and our own peculiar immigrant dreams.

For once Adam Sandler is going after a target he knows really well – our crazy American fantasy about Zionism. I found myself thinking back on my recent blog post about Jews versus Italians. True, American Jewish men in our culture are not supposed to be sexy. But Isreali Jewish men are. They are the warriors, rightful descendents of the Maccabees, and we look to them with a kind of fevered awe and cockeyed reverence. Sandler and company make perfect fun of that reverence.

I wonder what would happen if you were to edit these two films together, patching scenes from “The Savages” in with scenes from “Zohan”. The dark, understated indie character study, all calibrated silences and emotions too subtely devastating to speak aloud, sliced together with an over the top cultural farce about a comic superhero, absurdist icon for our time, blithely squirting Hummus over everything he sees with raw sexual abandon.

I think it could work.

Does anyone have any inspired ideas for other potential movie mashups?